Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Can you advise some good books covering areas which are required for serious probability theory studies (e.g. measure theory, functional analysis)? Preferably this book should have some problem sets to work on. Thanks!

share|improve this question
Should be community wiki. –  Jyotirmoy Bhattacharya Sep 26 '10 at 1:04
The answers should be cw as well. Or do they become automatically? –  Rasmus Sep 26 '10 at 14:47
Apparently only answers that appeared after the question was made cw become cw automatically. –  Rasmus Sep 26 '10 at 14:51

7 Answers 7

For a broad overview in one book at a graduate level, it is hard to beat Foundations of Modern Probability (Second edition) by Olav Kallenberg. His presentation is classroom tested, and many standard complicated proofs have been made very concise. I'm a big fan of this book!

share|improve this answer

Take a look at "Measure Theory and Probability" by A.K. Basu. This book has lots of problem sets in them and contains some serious probabilty theory. It developed measure theory with probability as the main application. Also through-out the book there are examples which were really helpful.

share|improve this answer
Good one! Thanks a lot! –  Alexey Kalmykov Sep 25 '10 at 18:56

Pollard, A User's Guide to Measure Theoretic Probability

share|improve this answer

Dudley, Real Analysis and Probability

share|improve this answer

Billingsley, Probability and Measure.

share|improve this answer
Why the downvote? –  Rasmus Sep 28 '10 at 10:31

A quite new and german one: Klenke, Wahrscheinlichkeitstheorie.

share|improve this answer
Also available in english: amazon.ca/Probability-Theory-Comprehensive-Achim-Klenke/dp/… (see Simon's answer). –  Rasmus Sep 28 '10 at 10:32

Jacod and protter is great.

Probability Theory: A Comprehensive Course by Klenke is worth looking at too.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.